This is Luka's side of the story, in her song, Lie.
She wants everything to be perfect. She wants them to be able to love each other, without the hurtful bullying and pain and brings. She tells herself that she doesn't need Gumi, she doesn't want Gumi, and eventually she'll forget Gumi. But she still loves her and she cannot hurt her, she plays along like everything is fine. She tells her she loves her. She realizes that she is breaking off though, she doesn't cry for Gumi anymore. She says it's wrong, she can't take it. She wants Gumi to be happy. She hopes Gumi cannot see this, she tells her they'll always be perfect. She begins an affair with a boy, she doesn't inform Gumi. She doesn't understand how Gumi doesn't see through her facade. She wants Gumi to love someone who loves her back. She wants to see Gumi smile. She wants her in the arms of someone that won't get her bullied. She wants someone for Gumi that is better than her. She loves Gumi still, and she doesn't want to put her through anymore pain.
There are 3 reasons this song could be called Lie:
1. She is lying to Gumi
2. She is lying to the boy (Kaito/Gakupo)
3. She is lying to herself